Problem: Rewrite as a simplified fraction. ${0.2\overline{8} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 28.8888...\\ 10x &= 2.8888...\end{align*}}$ Subtracting the two equations, we have: ${90x = 26}$ ${x = \dfrac{26}{90}} $ ${x = \dfrac{13}{45}} $